Combining the experimental techniques of high-resolution X-ray diffraction, magnetometry, specific heat measurement, and X-ray photoelectron, Raman and dielectric spectroscopy techniques, we have studied the influence of La and Cr doping on the crystal structure and magnetism of the room temperature Aurivillius multiferroic Bi5Ti3FeO15 by investigating the physical properties of (Bi4La)Ti3FeO15 and Bi5Ti3 (Fe0.5Cr0.5)O15. The parent (Bi5Ti3FeO15) and the doped ((Bi4La)Ti3FeO15 and Bi5Ti3(Fe0.5Cr0.5)O15) compounds crystallize in the A21am space group, which is confirmed through our analysis of high-resolution synchrotron X-ray diffraction data obtained on phase-pure polycrystalline powders. We determined the oxidation states of the metal atoms in the studied compounds as Fe3+, Ti4+, Cr3+, and La3+ through the analysis of X-ray photoelectron spectroscopy data. The magnetic susceptibilities of the three compounds are marked by the absence of a long-range ordered ground state, but dominated by superparamagnetic clusters with dominant antiferromagnetic interactions. This signature of short-range magnetism is also seen in specific heat as a low temperature enhancement which is suppressed upon the application of external magnetic fields up to 8 T. Our dielectric spectroscopy experiments showed that the three studied compounds display similar features in the dielectric constant measured as a function of frequency. However, upon doping La at the Bi site, the width of the ferroelectric hysteresis loop increases for (Bi4La)Ti3FeO15 compared to that of the parent compound Bi5Ti3FeO15, and with Cr doping, Bi5Ti3(Fe0.5Cr0.5)O15 becomes a leaky dielectric. The resilience of the Aurivillius crystal structure towards doping of La at the Bi site and Cr at the Fe site is clearly seen in the bulk properties of magnetic susceptibility, specific heat and the average crystal structure. The relevance of changes in the local structure is evident from our Raman spectroscopy and X-ray pair distribution function studies.